conditional_from_joint
std.stats.conditional_from_joint · Level L0The conditional distributions P(Y = j | X = i) = P(X = i, Y = j) / P(X = i) of a finite joint table, one row per value of X. Each row sums to 1; a row of zero mass has no conditional distribution.
P(Y = j | X = i) = pᵢⱼ / Σₖ pᵢₖ
Signature
conditional_from_joint(joint: f64[m, n]) → f64[m, n]
Structure
The function as NOVA stores it: one box per input, operation and output, and arrows that carry values. A double border marks another library function this one runs — called once, or by Scan once per element; select it to open that function.
- input
- operation
- constant
- call
- output
Verification
- Signature proven by NOVA’s shape solver, for every size.
- Equal to the reference
joint / joint.sum(axis=1, keepdims=True)in exact rational arithmetic, on all 40 test cases. - All 553 float64 results inside the running error bound; the closest uses 69% of it.
- Interpreter and NumPy backend return bit-identical results.
- At float32 too: the 40 test cases rounded to float32, and 40 of them inside the running error bound at u = 2⁻²⁴; the closest uses 58% of it.
Accuracy in detail
- correctly rounded (the float64 nearest the exact value)
- 79%
- bit-equal to the NumPy formula in float64
- 92%
- largest error, in units in the last place
- 1.84
Identity
sha256:36296235fb3a62d9044790710e3345a936e4118ed2ae50b43f6bfbf46b65f4aeThe semantic hash of the graph. It changes when the program changes, and never when only its documentation does.
Control handle
- Symbol
- Ω:std.stats.conditional_from_joint · Ω:conditional_from_joint
- Pins
sha256:5168e740de9e4fe4b5cedc71d755b043be1de135c1f4224d85273cc928c38e5athis graph alone- Evidence
sha256:eddd347a337abd780f573efa4b8454ac9214f56077f64d359e6503a930ad23cbthe hash of its verification record- Needs
- no capability: a pure function
Through NOVA’s control layer, the symbol launches this function only while the program still matches what it pins: a change to this graph, or to any graph it reaches, needs a migration first.